Help with Rockbass Corvette (active)

So i had noticed my input jack had been pretty loose, but couldn't find a way to tighten it. Then last night I lose all sound, and open it up to take a look.

First off, i find i can tighten my input. Go me.

Secondly, i see the wires leading from the battery to the jack have broken off. My friend said he'll solder it back on for me, but I want to confirm that this is the right thing to do first.

Now I know there are two wires leading off this battery (black ones). One doesn't seem to go anywhere (except i think it's other end branchs into the side of the bass, is this a ground wire?). The other wire, when touched to the jack, does make noise. So do I just solder this one wire to the jack, and let the other one alone? is there any specific place to attach it to?

Most active basses have a stereo jack, and the wire from the negative side of the battery is wired to the jack so when you plug the bass in (with a mono plug), the negative side of the battery is connected to the ground. (thats why the battery dies when you leave an active bass plugged in)
The wire from the positive side of the battery should be connected to the preamp.

So there should be three wires to the jack :
- your output signal (connected to the part of the jack hat makes contact with the tip of your instrument cable)
- the negative from the battery
- the ground (probably soldered to the back of a pot)